Recently, small-signal stability of the modular multilevel converter (MMC) based high-voltage direct current (HVDC) transmission for wind farm integration has attracted great attentions. The impedance-based frequency-domain method is an effective tool for such studies, in which the accuracy of the impedance model is of significant importance. Currently, the decoupled single-input single-output (SISO) sequence impedance of the MMC-HVDC system with wind farm is commonly used due to the simplicity in stability analysis. However, since both the MMC and wind farm exhibit frequency coupling behaviors, the decoupled SISO sequence impedance model may lead to inaccurate stability conclusion under certain conditions. In order to improve the model accuracy, based on the harmonic state-space (HSS) modeling approach, this paper proposes a generalized multi-input multi-output (MIMO) sequence impedance model of the MMC-wind farm system. The proposed MIMO impedance model can effectively capture the frequency couplings in the interconnected system, based on which the coupling mechanism of multi-frequency components within the MMC is then revealed. To facilitate the interconnection analysis, the model truncation criteria is proposed and validated by comparing the accuracy of the MIMO model with different truncated dimensions. In addition, this paper considers the internal impedance network of the wind farm when developing the aggregated wind farm impedance model for interaction stability analysis. Finally, the proposed MIMO sequence impedance model is applied to accurately predict the instability of the MMC-HVDC connected wind farm system.

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Conventional small-signal approaches present obvious advantages applied in analyzing closed-loop stability in power electronics systems. However, linearized models fall short of predicting any nonlinear behavior which means not able to acquire the accurate stability margin. This paper mainly analyzes bifurcation behaviors of the Modular Multilevel Converter (MMC) connected to a weak grid and calculates the parameters' precise stability margin. The nonlinear continuoustime averaging model of the MMC is established to study two common bifurcation phenomena, i.e. Saddle-Node bifurcation (SNB) and Hopf bifurcation (HB). Characteristics of limit cycles caused by HB are analyzed by changing the value of a certain parameter. The theoretical analysis has been validated by the time domain simulation results.

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With the wind power penetration rate continuously rising, a suitable wind farm model considering both accuracy and simplicity is required for power system stability analysis. To accomplish this goal, an accurate aggregated modified sequence impedance model of the wind farm is established in this paper. The modified sequence impedance model of wind turbine generator is established, which considers the coupling between the positive-and negative-sequence impedances. The modified sequence impedances of the ac collection system, transformers, and ac grid are also derived. In this way, the impedance network of the entire wind farm system can be formed and simplified to acquire the accurate aggregated modified sequence impedance. Furthermore, the proposed model is compared with the traditional single-machine aggregated model which shows the necessity of establishing the accurate aggregated model. It is worth noting that the differences among each wind turbine generator's operation points can be included in the proposed model. Compared with the results of impedance measurements of a target wind farm, the accuracy of the proposed aggregated sequence impedance model of the wind farm is verified in frequency domain. The application of the proposed model in the stability analysis of a grid-connected wind farm is also presented with consideration of the ac grid strength. What is more, the effect of the inertial controller on the wind farm system stability is also analyzed to make the impact of this study much more appealing and up to date.